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QUESTION 22 Show your logic clearly and completely so that other students in our class can...
Show all the work for the parts below. (Part B) Consider the function y = f(x)...
Show all the work for the parts below.
(Part B) Consider the function y = f(x) = Vx. (i) Construct the fourth degree Taylor polynomial for the cube root function centered at x = 1. How well does your polynomial approximate the value of V0.5? How well does your polynomial approximate the value of V9? (ii) Construct the fourth degree Taylor polynomial for the cube root function centered at x = 8. How well does your polynomial approximate the value...
8 pts . Answer parts a through e using the function f(x)- isd br cipah Tperpebynomia.ced0 Find th...
8 pts . Answer parts a through e using the function f(x)- isd br cipah Tperpebynomia.ced0 Find the eighth degree Taylor polynomial, centered at 0, to approximate f(x) a. . Be sure to simplify your answer. b. Using your eighth degree polynomial from part a and Taylor's Inequality, ii fork-als,the E find the magnitude of the maximum possible error on [0, .1]. x-ato (n 1)! c. Approximateusing your eighth degree Taylor polynomial. What is the actual 1.1 error? Is it...
Problem 4 Answer the following questions about f(1) = VI. (Show all details.) (a.) Find the...
Problem 4 Answer the following questions about f(1) = VI. (Show all details.) (a.) Find the degree n = 3 Taylor polynomial centered at a = 1 for the function f(x). (Don't use a table, show all work when determining the polynomial). (b.) Use your answer from (a.) to estimate V1.1. Do not simplify!
Question 4: Talyor. Maclaurin and Power Series For parts a, b, c and d, use the...
Question 4: Talyor. Maclaurin and Power Series For parts a, b, c and d, use the following function: f(x) = (-3x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.3. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state...
dont ans this question Euler's method is based on the fact that the tangent line gives...
dont ans this question
Euler's method is based on the fact that the tangent line gives a good local approximation for the function. But why restrict ourselves to linear approximants when higher degree polynomial approximants are available? For example, we can use the Taylor polynomial of degree about = No, which is defined by P.(x) = y(x) + y (xo)(x – Xa) + 21 (x- This polynomial is the nth partial sum of the Taylor series representation (te) (x –...
A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. You are permitted to use your calculator to...
A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in...
There are also approximations of higher order derivatives that can be computed using only values ...
Number 9 requires number 8 so please can you answer
both? Thanks. Here's more context:
There are also approximations of higher order derivatives that can be computed using only values of the original function. Consider the approximation: u(a + 2h)-2u(a + h) + u (a) h2 8. Using your knowledge of Taylor series, what derivative is approximated by Equa Many different combinations of terms can be used to create approximations to deriva- tion??? What is the order of the approximation?...
Hello, I am having trouble with part c of this question. Here is my work so far: The solution for part c states that a...
Hello, I am having trouble with part c of this question.
Here is my work so far:
The solution for part c states that a possible solution is (e^16
* 4^3) / 3!
I am having trouble understanding how they got e^16 or why they
decided to use e^(4^2) for M in the equation |f(x) - Tn(x)| <=
(M / (n + 1)!) * |x - 0|^(n + 1).
From my understanding, I have to maximize H^3(x) (i.e. 3rd
derivative...
Show clearly your steps answering requests below and upload a single file. (3 points each) (1)Use...
Show clearly your steps answering requests below and upload a single file. (3 points each) (1)Use a Riemann sum to estimate the area under the curve of the function f(x) = x2 - 6x + 10 between x = 0 and x = 8 using the midpoint rule with n= 2 subintervals. State the midpoints and other values that are used, and the answer. (2) Graph the above f (x) between x = 0 and x = 8, show the...
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand it...
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...
Show all the work for the parts below.
(Part B) Consider the function y = f(x) = Vx. (i) Construct the fourth degree Taylor polynomial for the cube root function centered at x = 1. How well does your polynomial approximate the value of V0.5? How well does your polynomial approximate the value of V9? (ii) Construct the fourth degree Taylor polynomial for the cube root function centered at x = 8. How well does your polynomial approximate the value...
8 pts . Answer parts a through e using the function f(x)- isd br cipah Tperpebynomia.ced0 Find the eighth degree Taylor polynomial, centered at 0, to approximate f(x) a. . Be sure to simplify your answer. b. Using your eighth degree polynomial from part a and Taylor's Inequality, ii fork-als,the E find the magnitude of the maximum possible error on [0, .1]. x-ato (n 1)! c. Approximateusing your eighth degree Taylor polynomial. What is the actual 1.1 error? Is it...
Problem 4 Answer the following questions about f(1) = VI. (Show all details.) (a.) Find the degree n = 3 Taylor polynomial centered at a = 1 for the function f(x). (Don't use a table, show all work when determining the polynomial). (b.) Use your answer from (a.) to estimate V1.1. Do not simplify!
Question 4: Talyor. Maclaurin and Power Series For parts a, b, c and d, use the following function: f(x) = (-3x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.3. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state...
dont ans this question
Euler's method is based on the fact that the tangent line gives a good local approximation for the function. But why restrict ourselves to linear approximants when higher degree polynomial approximants are available? For example, we can use the Taylor polynomial of degree about = No, which is defined by P.(x) = y(x) + y (xo)(x – Xa) + 21 (x- This polynomial is the nth partial sum of the Taylor series representation (te) (x –...
A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in...
Number 9 requires number 8 so please can you answer
both? Thanks. Here's more context:
There are also approximations of higher order derivatives that can be computed using only values of the original function. Consider the approximation: u(a + 2h)-2u(a + h) + u (a) h2 8. Using your knowledge of Taylor series, what derivative is approximated by Equa Many different combinations of terms can be used to create approximations to deriva- tion??? What is the order of the approximation?...
Hello, I am having trouble with part c of this question.
Here is my work so far:
The solution for part c states that a possible solution is (e^16
* 4^3) / 3!
I am having trouble understanding how they got e^16 or why they
decided to use e^(4^2) for M in the equation |f(x) - Tn(x)| <=
(M / (n + 1)!) * |x - 0|^(n + 1).
From my understanding, I have to maximize H^3(x) (i.e. 3rd
derivative...
Show clearly your steps answering requests below and upload a single file. (3 points each) (1)Use a Riemann sum to estimate the area under the curve of the function f(x) = x2 - 6x + 10 between x = 0 and x = 8 using the midpoint rule with n= 2 subintervals. State the midpoints and other values that are used, and the answer. (2) Graph the above f (x) between x = 0 and x = 8, show the...
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...
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